In Theorem REF , the term \(t\)  witnessing that \(b\)  belongs to the subalgebra generated by \(a_1,\dots ,a_k\) 
clearly has depth polynomial in \(n\) .
In the case that the \(\mathsf {d}\) -cube term is a Mal'tsev term, this was already observed in [1]}.
If the \(\mathsf {d}\) -cube term is a near-unanimity term, then the fact that \(b\)  belongs to the subalgebra generated by
\(a_1,\dots ,a_k\)  can be witnessed by polynomially many terms of constant length by the
Baker–Pixley Theorem [2]}.
It is however open in the general case, whether a polynomial bound can be imposed on the length of a representation
of \(t\)  by a term rather than by a circuit, as in Theorem REF .
